Advertisements
Advertisements
Question
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find Correlation coefficient between X and Y.
Solution
Here, `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3`
r = `+-sqrt("b"_"XY" * "b"_"YX")`
`= +- sqrt((- 0.3)(- 1.2))`
`= +- sqrt0.36 = +- 0.6`
Since bYX and bXY both are − negative,
r is also negative.
∴ r = −0.6
APPEARS IN
RELATED QUESTIONS
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of X for Y = 25.
You are given the following information about advertising expenditure and sales.
Advertisement expenditure (₹ in lakh) (X) |
Sales (₹ in lakh) (Y) | |
Arithmetic Mean | 10 | 90 |
Standard Mean | 3 | 12 |
Correlation coefficient between X and Y is 0.8
- Obtain the two regression equations.
- What is the likely sales when the advertising budget is ₹ 15 lakh?
- What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?
Bring out the inconsistency in the following:
bYX = bXY = 1.50 and r = - 0.9
For a certain bivariate data
X | Y | |
Mean | 25 | 20 |
S.D. | 4 | 3 |
And r = 0.5. Estimate y when x = 10 and estimate x when y = 16
The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)
Sales | Adv. Exp. | |
Mean | 40 | 6 |
S.D. | 10 | 1.5 |
Coefficient of correlation between sales and advertisement expenditure is 0.9.
What should be the advertisement expenditure if the firm proposes a sales target ₹ 60 crores?
For certain bivariate data the following information is available.
X | Y | |
Mean | 13 | 17 |
S.D. | 3 | 2 |
Correlation coefficient between x and y is 0.6. estimate x when y = 15 and estimate y when x = 10.
If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find
- `bar x`,
- `bar y`,
- bYX
- bXY
- r [Given `sqrt0.375` = 0.61]
The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.
The two regression lines between height (X) in inches and weight (Y) in kgs of girls are,
4y − 15x + 500 = 0
and 20x − 3y − 900 = 0
Find the mean height and weight of the group. Also, estimate the weight of a girl whose height is 70 inches.
Choose the correct alternative:
Both the regression coefficients cannot exceed 1
State whether the following statement is True or False:
If bxy < 0 and byx < 0 then ‘r’ is > 0
State whether the following statement is True or False:
Regression coefficient of x on y is the slope of regression line of x on y
If n = 5, ∑xy = 76, ∑x2 = ∑y2 = 90, ∑x = 20 = ∑y, the covariance = ______
The value of product moment correlation coefficient between x and x is ______
The geometric mean of negative regression coefficients is ______
The equations of two lines of regression are 3x + 2y – 26 = 0 and 6x + y – 31 = 0. Find variance of x if variance of y is 36
x | y | xy | x2 | y2 |
6 | 9 | 54 | 36 | 81 |
2 | 11 | 22 | 4 | 121 |
10 | 5 | 50 | 100 | 25 |
4 | 8 | 32 | 16 | 64 |
8 | 7 | `square` | 64 | 49 |
Total = 30 | Total = 40 | Total = `square` | Total = 220 | Total = `square` |
bxy = `square/square`
byx = `square/square`
∴ Regression equation of x on y is `square`
∴ Regression equation of y on x is `square`
The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.
x | y | |
Mean | 53 | 142 |
Variance | 130 | 165 |
`sum(x_i - barx)(y_i - bary)` = 1170